The provider is in the wrong here, any way you slice it.
As a provider I would NEVER take on a family that refused my consent to transport permission slip - it's actually one of my policies. But in this case the provider took on the family anyway - and even if the mom *said* they would pick up early on games days, that wouldn't have been good enough for me and it shouldn't have been good enough for the provider. Because we know how that story ends